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  Algebraic solutions of the Lam equation, revisited [1 citations — 0 self]

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by Robert S. Maier
J. Differential Equations
http://uranium.math.arizona.edu/~rsm/papers/paper104.ps
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Abstract:

A minor error in the necessary conditions for the algebraic form of the Lame equation to have a finite projective monodromy group, and hence for it to have only algebraic solutions, is pointed out. [See F. Baldassarri, "On algebraic solutions of Lame's differential equation", J. Differential Equations 41 (1) (1981), 44--58.] It is shown that if the group is the octahedral group S 4, then the degree parameter of the equation may differ by 1=6 from an integer; this possibility was missed. The omission affects a recent result on the monodromy of the Weierstrass form of the Lame equation. [See R. C. Churchill, "Two-generator subgroups of SL(2; C) and the hypergeometric, Riemann, and Lame equations", J. Symbolic Computation 28 (4--5) (1999), 521--545.] The Weierstrass form, which is a differential equation on an elliptic curve, may have, after all, an octahedral projective monodromy group.

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